$\dfrac{ -4v - 9w }{ 9 } = \dfrac{ -7v + x }{ 5 }$ Solve for $v$.
Solution: Multiply both sides by the left denominator. $\dfrac{ -4v - 9w }{ {9} } = \dfrac{ -7v + x }{ 5 }$ ${9} \cdot \dfrac{ -4v - 9w }{ {9} } = {9} \cdot \dfrac{ -7v + x }{ 5 }$ $-4v - 9w = {9} \cdot \dfrac { -7v + x }{ 5 }$ Multiply both sides by the right denominator. $-4v - 9w = 9 \cdot \dfrac{ -7v + x }{ {5} }$ ${5} \cdot \left( -4v - 9w \right) = {5} \cdot 9 \cdot \dfrac{ -7v + x }{ {5} }$ ${5} \cdot \left( -4v - 9w \right) = 9 \cdot \left( -7v + x \right)$ Distribute both sides ${5} \cdot \left( -4v - 9w \right) = {9} \cdot \left( -7v + x \right)$ $-{20}v - {45}w = -{63}v + {9}x$ Combine $v$ terms on the left. $-{20v} - 45w = -{63v} + 9x$ ${43v} - 45w = 9x$ Move the $w$ term to the right. $43v - {45w} = 9x$ $43v = 9x + {45w}$ Isolate $v$ by dividing both sides by its coefficient. ${43}v = 9x + 45w$ $v = \dfrac{ 9x + 45w }{ {43} }$